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If f:RtoR,defined by F(x)=1+x^2, then sh...

If `f:RtoR,`defined by `F(x)=1+x^2`, then show that f is neither 1 - 1 nor onto.

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If f : R to R defined by f(x) = 1+x^(2), then show that f is neither 1-1 nor onto.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Knowledge Check

  • If f:RtoR is defined by f(x)=x^(3) then f^(-1)(8)=

    A
    `{2,-2}`
    B
    `{2,2}`
    C
    `{2}`
    D
    `{2,omega,2omega^(2)}`

  • Let f: N rarr N be defined by f(x)=x^(2)+x+1 then f is

    A
    one-one, onto
    B
    many one onto
    C
    one-one but not onto
    D
    onto but not one-one

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